Order:
  1. Uniqueness of Logical Connectives in a Bilateralist Setting.Sara Ayhan - 2021 - In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2020. College Publications. pp. 1-16.
    In this paper I will show the problems that are encountered when dealing with uniqueness of connectives in a bilateralist setting within the larger framework of proof-theoretic semantics and suggest a solution. Therefore, the logic 2Int is suitable, for which I introduce a sequent calculus system, displaying - just like the corresponding natural deduction system - a consequence relation for provability as well as one dual to provability. I will propose a modified characterization of uniqueness incorporating such a duality of (...)
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  2.  36
    Logical Multilateralism.Heinrich Wansing & Sara Ayhan - 2023 - Journal of Philosophical Logic 52 (6):1603-1636.
    In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  3. A cut-free sequent calculus for the bi-intuitionistic logic 2Int.Sara Ayhan - manuscript
    The purpose of this paper is to introduce a bi-intuitionistic sequent calculus and to give proofs of admissibility for its structural rules. The calculus I will present, called SC2Int, is a sequent calculus for the bi-intuitionistic logic 2Int, which Wansing presents in [2016a]. There he also gives a natural deduction system for this logic, N2Int, to which SC2Int is equivalent in terms of what is derivable. What is important is that these calculi represent a kind of bilateralist reasoning, since they (...)
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  4.  22
    On Synonymy in Proof-Theoretic Semantics: The Case of \(\mathtt{2Int}\).Sara Ayhan & Heinrich Wansing - 2023 - Bulletin of the Section of Logic 52 (2):187-237.
    We consider an approach to propositional synonymy in proof-theoretic semantics that is defined with respect to a bilateral G3-style sequent calculus \(\mathtt{SC2Int}\) for the bi-intuitionistic logic \(\mathtt{2Int}\). A distinctive feature of \(\mathtt{SC2Int}\) is that it makes use of two kind of sequents, one representing proofs, the other representing refutations. The structural rules of \(\mathtt{SC2Int}\), in particular its cut rules, are shown to be admissible. Next, interaction rules are defined that allow transitions from proofs to refutations, and vice versa, mediated through (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  5.  20
    Introduction: Bilateralism and Proof-Theoretic Semantics (Part I).Sara Ayhan - 2023 - Bulletin of the Section of Logic 52 (2):101-108.
  6.  82
    What is the Meaning of Proofs?: A Fregean Distinction in Proof-Theoretic Semantics.Sara Ayhan - 2020 - Journal of Philosophical Logic 50 (3):571-591.
    The origins of proof-theoretic semantics lie in the question of what constitutes the meaning of the logical connectives and its response: the rules of inference that govern the use of the connective. However, what if we go a step further and ask about the meaning of a proof as a whole? In this paper we address this question and lay out a framework to distinguish sense and denotation of proofs. Two questions are central here. First of all, if we have (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  7. What are acceptable reductions? Perspectives from proof-theoretic semantics and type theory.Sara Ayhan - 2023 - Australasian Journal of Logic 20 (3):412-428.
    It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the same conclusion would have to be identified. In this paper it will be shown that the question, which reductions we accept in our system, is not only important if we see them as generating a theory of proof identity but is also (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  8. Meaning and identity of proofs in a bilateralist setting: A two-sorted typed lambda-calculus for proofs and refutations.Sara Ayhan - forthcoming - Journal of Logic and Computation.
    In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard correspondence, which has been well-established between the simply typed lambda-calculus and natural deduction systems for intuitionistic logic, and apply it to a bilateralist proof system displaying two derivability relations, one for proving and one for refuting. The basis will be the natural deduction system (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  9.  17
    Introduction: Bilateralism and Proof-Theoretic Semantics (Part II).Sara Ayhan - 2023 - Bulletin of the Section of Logic 52 (3):267-274.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark